Data and Probability: Practice Set 4
Data and Probability: Practice Set 4 is a mixed practice set that combines data-handling questions (reading tables, bar charts and pictograms, and calculating averages) with probability questions (expressing chance as a fraction, decimal or percentage). Papers group these two skills together because both rely on reading information carefully and working with parts of a whole, and this is the combined section format used in GL Assessment and CEM-style maths papers under time pressure.
Method
- Skim the whole set first to see whether data-reading or probability questions come first, since data questions often take longer to read.
- For each data question, check the axis labels, chart title or pictogram symbol key before answering, rather than guessing from the shape of the chart.
- For a direct 'read off' question, answer straight from the data without doing any extra calculation.
- For an average question, decide which average is asked for (mean, median, mode or range) and use the correct method for that one.
- For a probability question, count the total outcomes and the favourable outcomes, then write the probability as a fraction in its simplest form.
- Double check that every probability answer is between 0 and 1, and simplify fractions fully before writing a final answer.
- Save any combined question that uses a table or chart to work out a probability until last if you are short of time, since it draws on two skills at once.
Worked example
A bag contains 5 red counters, 3 blue counters and 2 green counters. A counter is picked at random. (a) What is the probability that it is blue? (b) What is the probability that it is NOT green? Give both answers as fractions in their simplest form.
- Find the total number of counters: 5 + 3 + 2 = 10.
- For (a), there are 3 blue counters, so the probability is 3/10. This cannot be simplified further, since 3 and 10 share no common factor other than 1.
- For (b), first find the probability of green: there are 2 green counters, so P(green) = 2/10 = 1/5.
- P(not green) = 1 - P(green) = 1 - 1/5 = 4/5.
- Check this a different way: 'not green' means red or blue, which is 5 + 3 = 8 counters out of 10, so 8/10 = 4/5, which matches.
Practice questions
Try each question, then tap to reveal the answer.
Q1A pictogram shows that each full symbol represents 4 books. The row for Year 5 has 3 full symbols and one half symbol. How many books does Year 5 have?Show answer
Answer: 3 x 4 = 12, plus half of 4 = 2, so 12 + 2 = 14 books.
Q2Find the mean of 4, 7, 9, 12, 18.Show answer
Answer: Sum = 4 + 7 + 9 + 12 + 18 = 50. Mean = 50 / 5 = 10.
Q3A spinner has 8 equal sections numbered 1 to 8. What is the probability of spinning a number greater than 6?Show answer
Answer: Numbers greater than 6 are 7 and 8, so 2 out of 8 = 2/8 = 1/4.
Q4The range of a set of five numbers is 15. The smallest number is 8. What is the largest number?Show answer
Answer: Largest = smallest + range = 8 + 15 = 23.
Q5A bar chart shows 6 students chose football, 4 chose swimming and 2 chose tennis. If a student is picked at random from these 12, what is the probability they chose swimming?Show answer
Answer: 4/12 = 1/3.
Q6Find the median of 3, 8, 5, 8, 2, 9, 6.Show answer
Answer: Ordered: 2, 3, 5, 6, 8, 8, 9. The middle (4th of 7) value is 6.
Q7A fair coin is flipped twice. What is the probability of getting two heads?Show answer
Answer: 1/2 x 1/2 = 1/4.
Q8A pie chart shows that half of a class of 30 students chose blue as their favourite colour. How many students chose blue?Show answer
Answer: Half of 30 = 15 students.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
The table shows how 24 students travel to school: Walk 10, Bus 6, Car 5, Bike 3. (a) What fraction of the students travel by car? Give your answer in its simplest form. (b) If a student is picked at random, what is the probability that they do NOT walk?
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A box contains 20 balls, some red and some yellow. The probability of picking a red ball at random is 0.35. (a) How many red balls are in the box? (b) How many yellow balls are in the box? (c) A red ball is removed and not replaced. What is the new probability, as a fraction in its simplest form, of picking a red ball at random?
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Free printable worksheet
Want more practice on paper? Download the data and probability: practice set 4 worksheet pack - 12 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 21 of 11+ Maths Workbook 3, the whole course as one free printable PDF.
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